Assignments 00 1. Plot the curve x + y' = 6xy together with the tangent to the curve at the point 3 3 2. Calculate the derivative of the function f (x) =- 2 - 5 x + 2 and plot the function and its derivative on the same graph. Describe the relationship between the two graphs. 3. Let k denotes the number of letter in your first name (i.e., one named "Thomas" uses k =6). Define the function f (x) = 1- kx 1 + x 2 (a) Calculate f '(x), f " (x), f' (x), f4 (x). (b) Make a plot of both the function f(x) and its derivative f '(x) on the same window. Explain how the sign of derivative is related to the graph of f (x) . (c) Use the solve command to find the x-coordinates of all of the points on the graph of f(x) where the derivative equals to 0. Next find the y-coordinates of these points on the graph of f (x) . 4. Suppose f(x) = x + 2 x + 1 and the point P( - 3, 4) (a) Find the derivative of f (x) at the point P using the definition of a derivative. (b) Using the result in part (a), find an equation of tangent line to the graph of f (x) at the point. _(c) Display the graph of f (x) and the tangent line on the same coordinate system. 5. Use MAPLE to find the derivative of the function f(x) = 2 x cos(x) - 2 sin(x)